First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients

Aziz Harman, Ezgi Harman and Nan-Jing Huang

Journal of Mathematics, 2020, vol. 2020, 1-4

Abstract: For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1019038

DOI: 10.1155/2020/1019038

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